The FDPIC has updated (apparently on May 8, 2018) the information on the GDPR made available on its website (Link to PDF). It states, among other things, that the GDPR applies in international-local terms if there is an establishment in the territory of the EU [or other countries of the EEA] or if the data processing is related to the targeting of offers or behavioral monitoring. On-site data processing by an independent processor is no longer mentioned.